Question

A person can row 8 km upstream and 24 km downstream in 4 hours. He can row 12 km downstream and 12 km upstream in 4 hours. Find the speed of the person in still water as also the speed of the current

Answer 1

LET SPEED OF BOAT IN STILL WATER BE X AND THAT OF CURRENT BE Y (BOTH IN KMPH)

TIME = DISTANCE / SPEED

SO 8/(X-Y)+24/(X+Y)=4 OR 2/P+6/Q=1 WHERE P=X-Y Q=X+Y

ALSO 12/(X+Y)+12/(X-Y)=4 OR 3/P+3/Q=1

SOLVING THE EQUATIONS WE HAVE P=4 Q=12

SO X=8 Y=4 

SO SPEED OF PERSON IN STILL WATER IS 8 KMPH AND THAT OF CURRENT IS 4 KMPH

Answer 2

Answer:

Y = 4 and X = 8

Step-by-step explanation:

Let the speed of rowing in still water = x km/hr

Let the speed of current = y km/hr

Speed of boat in upstream is (x - y) km/hr

Speed of boat in downstream is (x + y) km/hr

Distance = Speed x time

Time = Distance/Speed

Thus, the equations will be:

8/(x-y) + 24/(x + y) = 4 ............ (1)

12/(x-y) + 12/(x + y) = 4 ............ (2)

Now the above equations will be reduced in linear form

 Let 1/(x-y) = A

and 1/(x+y) = B  

So the new equations will be:

8A + 24B = 4 ............(3)

12A + 12B = 4 ............(4)

On multiplying eq. (4) by 2 and then subtracting from eq. (3), we get

-16A = -4

A = 1/4 --------- (5)

On putting  value of "A" in eq. (4) , we get,

3 + 12 B = 4

B = 1/12 ------------ (6)

Now we know that A = 1/( x-y) and B = 1/​(x+y)

On putting values of "A" and "B" we get:

1/( x-y) = 1/4

( x-y) = 4 ---------- (7)

1/( x+y)= 1/12  

x + y = 12 ------- (8)

On adding eq. (7) and (8), we get:

2x = 16

x = 8 ----- (9)

On putting value of "x" in eq. (8), we get

y = 4